The kind of transparency I'm seeing in Ubuntu 11.10 is it will show the desktop wallpaper. This is not what I want.

When I first installed Ultimate Edition, transparent windows would show the window right below them, not the desktop. This is the kind of transparency that I want. How can I get Ubuntu to function like this again?

But, before I turned on compositing, I wasn't getting pseudo-transparency, either (which is what you're describing). If you're early enough in the set up process, it might be worth installing Ubuntu 11.10 fresh, and adding Xfce4 manually. I've had much better results doing it that way in the past. (for both 10.04 and 11.10)

Ultimate Edition uses to come pre-installed with compiz and its plugins.

You need to install Compiz and check if the default plugins includes those needed to enable transparent windows, such as "Opacity, Brightness and Saturation", which controls the transparency of the windows, "Opacify" reduces/increases the opacity of the window based on the mouse over windows behavior.

After you have done what Geppettvs D'Constanzo said, you can hold down alt over the window you want to make transparent, then scroll. It works wonderfully and you can see any non-minimized windows beneath. I hope it will work for you in XFCE!